New identities for linearized gravity on the Kerr spacetime

Aksteiner, S.Max Planck Gesellschaft zur Förderung der Wissenschaften e.V. (MPG),Max Planck Society for the Advancement of Science (MPG),Albert Einstein Institute, Potsdam, Germany (författare)

Funding Agency:EP/J011142/1
In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor M-ab which solves the linearized Einstein equations. The identity makes this manifest by relating M-ab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of M-ab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.

Andersson, L.Max Planck Gesellschaft zur Förderung der Wissenschaften e.V. (MPG),Max Planck Society for the Advancement of Science (MPG),Albert Einstein Institute, Potsdam, Germany (författare)
Bäckdahl, Thomas,1980Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Edinburgh,Örebro universitet,Örebro University,Chalmers tekniska högskola,Chalmers University of Technology,Institutionen för naturvetenskap och teknik,Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden; The University of Edinburgh, Edinburgh, United Kingdom(Swepub:oru)tsbl (författare)
Max Planck Gesellschaft zur Förderung der Wissenschaften e.V. (MPG)Albert Einstein Institute, Potsdam, Germany (creator_code:org_t)

Av författaren/redakt...: Aksteiner, S.; Andersson, L.; Bäckdahl, Thomas ...

Om ämnet

Av lärosätet: Göteborgs universitet; Chalmers tekniska högskola; Örebro universitet

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